(************** Content-type: application/mathematica **************)

Notebook[{
Cell[BoxData[{
    RowBox[{
      StyleBox[\( (*\ 
          carry\ out\ the\ forward\ and\ backward\ moves\ and\ the\ various\ \
rotations\ by\ updating\ the\ global\ location\ ' 
            Lpos'\ and\ direction\ angle\ ' \(\(Ltheta'\)\(.\)\)\ *) \),
        FormatType->StandardForm], 
      StyleBox[" ",
        FormatType->StandardForm], 
      StyleBox[\(\(\(Lmove[\ z_String, \ Ldelta_\ ]\  := \ 
            Switch[\ z, \ "\<+\>", \ \(Ltheta\  += \ 
                  Ldelta;\), \ "\<-\>", \ \(Ltheta\  -= \ 
                  Ldelta;\), \ "\<F\>", \ 
              Lpos\  += \ {Cos[Ltheta], \ Sin[Ltheta]}, \ "\<B\>", \ 
              Lpos\  -= \ {Cos[Ltheta], \ Sin[Ltheta]}, \ _\ , \ 
              Lpos\  += \ 
                0. \ ]\) \); \ \(\(LSystem::usage\  = \ "\<LSystem[axiom, \
{rules}, n, Ldelta:90 Degree] creates the L-string for the nth iteration of \
the list 'rules', starting with the string 'axiom'.\>"\) \); \  (*\ 
          make\ the\ \(string : \ starting\ with\ ' axiom'\), \ 
          use\ StringReplace\ the\ specified\ number\ of\ times\ *) \ \
\(\(LSystem[\ axiom_, \ rules_List, \ n_Integer, \ 
              Ldelta_:  N[90\ Degree]]\  := \ 
            Nest[\ StringReplace[#, \ rules] &, \ axiom, \ 
              n\ ]\) \); \ \(\(Off[General::spell1]\) \); \  (*\ 
          initialize\ the\ position\ ' Lpos'\ and\ the\ direction\ angle\ ' 
            Ltheta'; \ 
          create\ the\ Line\ graphics\ primitive\ represented\ by\ the\ L - 
            system\ by\ mapping\ ' 
              Lmove'\ over\ the\ characters\ in\ the\ L - string, \ 
          deleting\ all\ the\ Nulls; \ 
          then\ show\ the\ Graphics\ object\ *) \ \(\(LShow[lstring_String, \ 
              Ldelta_:  N[90\ Degree]]\  := \ \((Lpos = {0. , 0. }; \ 
              Ltheta = 0. ; \ 
              Show[\ Graphics[
                  Line[\ Prepend[\ 
                      DeleteCases[\ 
                        Map[Lmove[#, \ Ldelta] &, \ Characters[lstring]], \ 
                        Null\ ], \ {0, 0}]]], \ 
                AspectRatio\  -> \ Automatic])\)\) \); \  (*\ 
          same\ as\ above, \ 
          plus\ a\ list\ of\ colors\ for\ each\ segment\ contained\ in\ ' \
\(\(templist'\)\ --\)\ unfortunately, \ \(\('\) \(templist'\)\(\ \)\(isn'\) \
\(t\)\(\ \)\(really\ '\) \(temp'\)\), \ 
          but\ stays\ in\ memory\ as\ a\ global\ variable; \ 
          so\ sue\ me\ *) \ \(\(LShowColor[lstring_String, \ 
              Ldelta_:  N[90\ Degree]]\  := \ \((Lpos\  = \ {0. , \ 0. }; \ 
              Ltheta\  = \ 0. ; \ 
              templist\  = \ 
                Map[\ Line, \ 
                  Partition[\ 
                    Prepend[\ 
                      DeleteCases[\ 
                        Map[\ Lmove[#, \ Ldelta] &, \ 
                          Characters[lstring]\ ], \ Null], \ {0, 0}], \ 2, 
                    1]]; \ ncol\  = \ N[Length[templist]]; \ 
              huelist\  = \ Table[\ Hue[k/ncol], \ {k, \ 1. , \ ncol}\ ]; \ 
              Show[\ Graphics[\ 
                  N[Flatten[Transpose[{huelist, \ templist}]]]], \ 
                AspectRatio\  -> \ Automatic])\)\) \); \ \(\(On[
            General::spell1]\) \); \ \(\(LShowColor[\  (*\ Koch\ curve\ *) \ 
            LSystem["\<F\>", \ {"\<F\>"\  -> \ "\<F+F--F+F\>"}, \ 4], \ 
            N[60\ Degree]]\) \); \ \(\(LShowColor[\  (*\ Peano\ curve\ *) \ 
            LSystem["\<F\>", \ {"\<F\>"\  -> \ "\<F+F-F-F-F+F+F+F-F\>"}, \ 
              4]]\) \); \ \(\(LShowColor[\  (*\ Quadratic\ Koch\ island\ *) \ 
            LSystem["\<F+F+F+F\>", \ {"\<F\>"\  -> \ "\<F-F+F+FFF-F-F+F\>"}, \
\ 3]]\) \); \ \(\(LShowColor[\  (*\ 32 - segment\ curve\ *) \ 
            LSystem["\<F+F+F+F\>", \ {"\<F\>"\  -> \ \
"\<-F+F-F-F+F+FF-F+F+FF+F-F-FF+FF-FF+F+F-FF-F-F+FF-F-F+F+F-F+\>"}, \ 
              2]]\) \); \ \(\(LShowColor[\ 
            LSystem["\<YF\>", \  (*\ 
                Sierpinski\ arrowhead\ *) \ {"\<X\>"\  -> \ "\<YF+XF+Y\>", \ \
"\<Y\>"\  -> \ "\<XF-YF-X\>"}, \ 7], \ 
            N[60\ Degree]]\) \); \ \(\(LShowColor[\  (*\ 
              Peano - Gosper\ curve\ *) \ 
            LSystem["\<FX\>", \ {"\<X\>"\  -> \ "\<X+YF++YF-FX--FXFX-YF+\>", \
\ "\<Y\>"\  -> \ "\<-FX+YFYF++YF+FX--FX-Y\>"}, \ 4], \ 
            N[60\ Degree]]\) \); \ \(\(LShowColor[\  (*\ 
              Sierpinski\ triangle\ *) \ 
            LSystem["\<FXF--FF--FF\>", \ {"\<F\>"\  -> \ "\<FF\>", \ "\<X\>" -> \
"\<--FXF++FXF++FXF--\>"}, \ 6], \ N[60\ Degree]]\) \); \ \(\(LShowColor@
            LSystem["\<F+XF+F+XF\>", \  (*\ 
                Square\ curve\ *) \ {"\<X\>" -> "\<XF-F+F-XF+F+XF-F+F-X\>"}, \
\ 4]\) \); \ \(\(LShowColor[\  (*\ Dragon\ curve\ *) \ 
            LSystem["\<FX\>", \ {"\<X\>" -> "\<X+YF+\>", \ "\<Y\>" -> \
"\<-FX-Y\>"}, \ 12]]\) \); \ \(\(LShowColor@
            LSystem["\<L\>", \  (*\ 
                Hilbert\ curve\ *) \ {"\<L\>"\  -> \ "\<+RF-LFL-FR+\>", \ \
"\<R\>"\  -> \ "\<-LF+RFR+FL-\>"}, \ 6]\) \); \ 
        LShowColor@
          LSystem["\<X\>", \  (*\ 
              Hilbert\ curve\ II\ *) \ {"\<X\>"\  -> \ \
"\<XFYFX+F+YFXFY-F-XFYFX\>", \ "\<Y\>"\  -> \ "\<YFXFY-F-XFYFX+F+YFXFY\>"}, \ 
            3];\),
        FormatType->StandardForm]}], "\[IndentingNewLine]", 
    RowBox[{\(LShowColor[\ \ LSystem["\<F\>", \ {"\<F\>"\  -> \ \
"\<F+F--F+F\>"}, \ 4], \ N[86\ Degree]];\), " "}]}], "Input"]
}
]